H∞Control of the Actively Controlled Systems With Input Time Delay Based on CHsCTA Model Transformation

This study addresses the
$H_{\infty }$
control design problem for actively controlled systems with input time delay. A novel control algorithm is proposed to derive the
$H_{\infty }$
controller. The core concept involves employing the Chebyshev spectral continuous-time approximation (CHsCTA) and defining specific augmented matrices to reconfigure the original time-delayed system into a transformed system that is free of time delay. Subsequent control design is executed on this transformed system, facilitating the derivation of an
$H_{\infty }$
controller. Case studies demonstrate that compared with the existing Lyapunov-Krasovskii (L-K) functional-based algorithms, the proposed control algorithm is distinguished by its reduced conservatism and enhanced
$H_{\infty }$
control performance.